458 
Int. runoff 
Sat. runoff 
S*- 
1 ep 
fi A fe 
7^1 
1 
~l 
1 
: 0sz 
surface zone 
\ 
Zsz 
1 
1 
\ 
1 
1 
etz(z) \ 
9 
1 
Ztz 
Vc 
transmission zone 
2 
\ 
1 1 
Figure 1: Schematic representation of the local water balance model. 
flow is assumed to be of negligible importance in this version of the model. 
2.1 Local Water Balance Model 
Figure 1 depicts a schematic representation of the various soil moisture fluxes at a grid element. To 
allow for dynamic simulation of critical state variables such as surface soil moisture, the unsaturated 
zone is divided into two regions—the surface zone and the transmission zone. The surface zone is 
subjected to high-frequency atmospheric forcings which result in rapid change of moisture content. 
Consequently, a continuous water accounting is maintained in this zone whose depth is related to 
the penetration depth of the remote sensor used in soil moisture monitoring. For the transmission 
zone, the effects of the rapidly varying boundary conditions are usually damped out by the overlying 
medium. We will assume that the moisture state in the transmission zone has achieved a steady flow 
condition. The computation of various vertical soil moisture fluxes and runoff are described below. 
2.1.1 Infiltration. The infiltration rate, /,, is taken as the minimum of the infiltration capacity, 
/*, and the precipitation rate p: 
fi = min [f*,p] (1) 
To estimate the infiltration capacity, we employ the time condensation approximation (Ibrahim 
and Brutsaert, 1968; Milly, 1986) on the Philip’s solution (1957) to an initially uniform moisture 
profile subjected to a step change in soil moisture at the soil surface. As a result, f* depend only 
on cumulative infiltration in the surface zone, Fi, and the initial condition at the start of a rainfall 
event: 
f: = a 0 
4a 0 f;\ 
% ) 
1/2 
( 2 ) 
where Si is the sorptivity and Aq is a constant term which accounts for the effect of gravity. Employing 
the results of Eagleson’s (1978) synthesis of work on nonlinear diffusion by Crank (1975), Milly (1986) 
has evaluated Si and Aq from the case of infiltration into a soil that is i-nit.ia.11y dry, and obtained the 
following expressions: 
Aq 
(3) 
where 9 U re] 
minus entra] 
moisture diff 
2.1.2 Percoli 
ing the inter 
characterise 
estimated us 
where g is tl 
for percolati 
is the tensic 
distribution 
2.1.3 Exfiltr 
f e , by takini 
Neglect 
tration capa 
at the start 
where S e is 
2.1.4 Runoj 
Saturation < 
jacent to tl 
Infiltration 
is carried o 
summing tl 
the subsurf 
2.2 Water 
Given t 
scheme sim 
scale hydro 
spatially-di 
resented b]